This paper devotes to a feedback control strategy for nonlinear stochastic dynamical system to track a prespecified stationary response probability density. The system description and control design are conducted in Hamiltonian framework, and the excitations are confined to Gaussian white noises. The control design consists of several successive steps: firstly, separating the control into conservative and dissipative components by physical intuition, and expanding two components as polynomials; secondly, deriving the low-dimensional averaged equations of controlled Hamiltonian by stochastic averaging, and obtaining the stationary probability density of controlled responses by solving the associated Fokker-Planck-Kolmogorov (FPK) equation; thirdly and finally, determining the polynomial coefficients by minimising the performance index which balances the tracking performance and control cost. Two examples, i.e. Duffing oscillator and frictional system are adopted to illustrate the application and efficacy of this control strategy to track Gaussian and non-Gaussian response probability density.

本文致力于非线性随机动力系统的反馈控制策略，以跟踪预先指定的平稳响应概率密度。系统描述和控制设计在哈密​​顿框架下进行，并且激励仅限于高斯白噪声。控制设计由几个连续的步骤组成：首先，通过物理直觉将控制分成保守分量和耗散分量，并将两个分量展开为多项式；其次，通过随机平均推导受控哈密顿量的低维平均方程，通过求解相关的Fokker-Planck-Kolmogorov(FPK)方程得到受控响应的平稳概率密度；最后，通过最小化性能指标来确定多项式系数，从而平衡跟踪性能和控制成本。两个例子，即